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Which sign makes the statement true? $\newline$ $6.4 \times 10^3$ $\text{?}$ $640$ $\newline$ Choices: $\newline$ (A) $>$ $\newline$ (B) $<$ $\newline$ (C) $=$

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Compare numbers written in scientific notation

Full solution

Q. Which sign makes the statement true?

\newline

6.4 \times 10^3

\text{?}

640

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Express in Standard Form: We have $6.4 \times 10^3$ and $640$ . Let's first express both numbers in standard form to make them easier to compare. $\newline$ $6.4 \times 10^3$ is already in standard form. $\newline$ $640$ can be written as $6.4 \times 10^2$ because $640 = 6.4 \times 100$ and $100 = 10^2$ .
Compare Exponents: Now we compare $6.4 \times 10^3$ with $6.4 \times 10^2$ . Since the base number $6.4$ is the same in both expressions, we only need to compare the exponents of $10$ . The exponent $3$ in $10^3$ is greater than the exponent $2$ in $10^2$ . Therefore, $6.4 \times 10^3$ is greater than $6.4 \times 10^2$ .
Final Comparison: Since $6.4 \times 10^2$ is equivalent to $640$ , we can now write the comparison as: $\newline$ $6.4 \times 10^3 > 640$ $\newline$ So the correct sign to make the statement true is ＂ $>$ ＂.

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